• # Matrix Multiplication

A matrix is a set or real or complex numbers known as elements arranged in rows and columns to form a rectangular array of numbers to represent some kind of data. The rows and columns are also known as the dimensions of the matrix.
The number of rows is indicated by the letter m and the number of columns is indicated by the letter n, a matrix of such dimensions will be call an (m × n), read (m by n) matrix. If m=1, then the matrix is known as a row vector, and if n=1, then the matrix is known as a column vector.
To multiply two matrices, the number of rows in the second matrix must match the number of columns in the first matrix. This is shown in the Fig to the far right.
The Fig to the right shows a typical m*n matrix and how the elements are labeled, each element is suffixed by m and n as in amn. The Fig in the middle shows how to multiply two matrices. In the product matrix, each element is the sum of the elements of a row from the first matrix multiplied by the elements of a column from the second matrix, colour marked in the middle Fig.

Use the following tool to multiply two matrices.

## How to multiply two Matrices   ## Matrices Multiplication Tool

The following program allows the user to multiply two matrices.

### How to use the program:

Enter the dimensions of the two matrices, which are indicated by Matrix A m*n and Matrix B n*p below. For Matrix A, the top row, enter the dimensions m and n. For matrix B, enter the dimension p only, note: n must have the same value as n from matrix A, therefore it is automatically filled in when n from matrix A is entered.

m =   n =

n =   p =